Ship is so far assumed to be in calm water to determine, - stability of ship - EHP calculation through Froude expansion Ship usually, however, encounters.

Similar presentations

Presentation on theme: "Ship is so far assumed to be in calm water to determine, - stability of ship - EHP calculation through Froude expansion Ship usually, however, encounters."— Presentation transcript:

1
Ship is so far assumed to be in calm water to determine, - stability of ship - EHP calculation through Froude expansion Ship usually, however, encounters waves in the sea. Ship will respond due to wave action. Excitation Wave Wind Response Input output Motions Structural load 8.1 Seakeeping

4
Wind Generated Wave Systems The size of these wave system is dependent on the following factors. Wind Strength : - The faster the wind speed, the larger energy is transfer to the sea. - Large waves are generated by strong winds. Wind Duration : - The longer wind blow, the greater the time the sea has to become fully developed at that wind speed. Waves

5
Wind Generated Wave Systems Water Depth : - Wave heights are affected by water depth. - Waves traveling to beach will turn into breaking wave by a depth effect. Fetch - Fetch is the area of water that is being influenced by the wind. - The larger the fetch, the more efficient the energy transfer between wind and sea. Waves

10
t (sec) Frequency,   - The number of radians completed in 1 second (here the wave completes 9.43 radians in 1 second, or 3  … = to 1.5 times around the circle) 1  = 2  T     is given in RADIANS/sec Waves

11
 n = 2  T  n = k m These two formulas for frequency are also referred to as the Natural Frequency, or the frequency that a system will assume if not disturbed: Where k = spring constant (force/ length compressed/ stretched) Waves

12
t (sec) T Displacement, Z  - The distance traveled at a given time, t - Z o reflects the starting position - Z will be cyclical…it will not be ever-increasing 1 …This will give you the height of the wave or the length of the elongation / compression in a spring at a given time Z = Z o Cos(  n t) + Z o - Z o Z Waves

13
Wave Superposition Waves

14
Superposition Theorem The configuration of sea is complicated due to interaction of different wave systems. (Irregular wave) The complicated wave system is made up of many sinusoidal wave components superimposed upon each other. Fourier Spectral Analysis Waves

17
8.3 Simple Harmonic Motion Condition of Simple Harmonic Motion +a -a - Linear relation : The magnitude of force or moment must be linearly proportional to the magnitude of displacement - Restoring : The restoring force or moment must oppose the direction of displacement. a A naturally occurring motion in which a force causing displacement is countered by an equal force in the opposite direction. - It must exhibit a LINEAR RESTORING Force

18
Tension Compression - If spring is compressed or placed in tension, force that will try to return the mass to its original location  Restoring Force - The magnitude of the (restoring) force is proportional to the magnitude of displacement  Linear Force Simple Harmonic Motion

21
Spring-Mass-Damper System spring mass damper - Equation of motion (Free Oscillation) & Solution C : damping coefficient The motion of the system is affected by the magnitude of damping.  Under damped, Critically damped, Over damped If left undisturbed, these systems will continue to oscillate, slowly dissipating energy in sound, heat, and friction - This is called free oscillation or an UNDAMPED system Simple Harmonic Motion

22
Spring-Mass-Damper System - Under Damped : small damping, several oscillations - Critically Damped : important level of damping, overshoot once - Over damped : large damping, no oscillation No-Damping Under damped Critically damped Over damped Simple Harmonic Motion

24
Forcing Function and Resonance Unless energy is continually added, the system will eventually come to rest An EXTERNAL FORCING FUNCTION acting on the system - Depending on the force’s application, it can hinder oscillation - It can also AMPLIFY oscillation When the forcing function is applied at the same frequency as the oscillating system, a condition of RESONANCE exists Simple Harmonic Motion

26
Forcing Function & Resonance Condition 1- The frequency of the forcing function is much smaller than the system Displacement, Z = F/k Condition 2- The frequency of the forcing function is much greater than the system Z = 0 Condition 3- The frequency of the forcing function equals the system Z = infinity THIS IS RESONANCE! Simple Harmonic Motion

30
Encounter Frequency - Motion created by exciting force in the spring-mass-damper system is dependant on the magnitude of exciting force (F) and frequency (w). - Motion of ship to its excitation in waves is the same as one of the spring-mass-damper system. - Frequency of exciting force is dependent on wave frequency, ship speed, and ship’s heading. Ship Response

31
Encounter Frequency Crest V V Wave direction V Ship Response

32
Encounter Frequency Conditions - Head sea : A ship heading directly into the waves will meet the successive waves much more quickly and the waves will appear to be a much shorter period. - Following sea : A ship moving in a following sea, the waves will appear to have a longer period. - Beam sea : If wave approaches a moving ship from the broadside there will be no difference between wave period and apparent period experienced by the ship Ship Response

35
Heave Motion Restoring force in heave The restoring force in heave is proportional to the additional immersed distance. The magnitude of the restoring force can be obtained using TPI of the ship. Restoring force Ship Response

42
Resonance of Simple Harmonic Motion HeavePitch Roll Amplitude Resonance : Encounter freq.  Natural freq. Heave & Pitch are well damped due to large wave generation. Roll amplitude are very susceptible to encounter freq. And roll motions are not damped well due to small damping. Resonance is more likely to occur with roll than pitch & heave. Thus anti-rolling devices are necessary. Ship Response

43
Non-Oscillatory Dynamic Response Caused by relative motion of ship and sea. Shipping Water (deck wetness) : caused by bow submergence. Forefoot Emergence : opposite case of shipping water where the bow of the ship is left unsupported. Slamming : impact of the bow region when bow reenters into the sea. Causes severe structural vibration. Racing : stern version of forefoot emergence. Cause the propeller to leave the water and thus cause the whole ship power to race (severe torsion and wear in shaft). Added Power : The effects of all these responses is to increase the resistance. Ship Response

50
You are OOD on a DD963 on independent steaming in the center of your box during supper. You are doing 10kts on course 330 º T and the waves are from 060 º T with a period of 9.5 sec. The Captain calls up and orders you to reduce the Ship ’ s motion during the meal. Your JOOD proposes a change to course 060 º T at 12 kts. Do you agree and why/why not? The natural frequencies for the ship follow:  roll = 0.66 rad/s  longbend = 0.74 rad/s  pitch = 0.93 rad/s  torsion = 1.13 rad/s  heave = 0.97 rad/s